Symmetries of Julia sets of nondegenerate polynomial skew products on \(\mathbb{C}^{2}\) (Q977113)

The paper originates from the idea that the Julia sets of any kind of functions and maps can have symmetries. For the Julia set of a polynomial the symmetries are rotations. This problem being solved i.e. determination of the group of symmetries and of the polynomials having the same Julia set, the paper deals with the same problem in two dimensions. There are considered non-degenerate polynomials skew products in \(\mathbb{C}^2\), existence of vertical Green functions and Böttcher functions of the map, symmetries of the Julia set. It is then shown that the suitable transformations preserving the Julia set are conjugate to the rotational product map. A necessary and sufficient condition is given for the group of symmetries to be infinite.